2026 AHS P2 Q13

The above diagram shows part of the curve \(y=\dfrac{20}{2x-3}-1\) passing through the point \(P(4,3)\).

The curve meets the \(x\)-axis at the point \(Q(11.5,0)\). The tangent to the curve at \(P\) meets the \(x\)-axis at the point \(R\).

1. Show that the \(x\)-coordinate of \(R\) is \(5.875\).[4]
2. Find the shaded area \(PQR\).[4]